#### Answer

The system of equations associated to this matrix is inconsistent - it has no solutions.

#### Work Step by Step

The system associated with this matrix is
\begin{align*}
x_1+2x_2\qquad+x_4=&3\\
x_2+3x_3\qquad=&1\\
x_3+2x_4=&0\\
0=&2
\end{align*}
Since we know that in fact $0\neq2$ we see that this system is inconsistent and cannot have any solutions.